To minimize the risks associated with the drilling process, particular significance is presently attached to optimal planning of drilling process, in particular for oil and gas deposits where high-temperature high-pressure conditions are probable. A standard practice is to construct a mathematical Earth model for a subsurface area of interest so as to predict the evolution of target characteristics and properties during drilling process on the basis of the model and available log data. The model-based prediction is used for optimization of the drilling process. To provide accurate prediction, the earth model should preferably allow calculations directly in the drilling process, i.e. in real-time, and enable earth model calibration or adjustment while drilling on the basis of log data acquired in the drilling process, so as to permit prediction not only before, but also in real-time during the drilling process.
Presently there are two groups of standard technologies aimed at overpressure simulation, investigation and prediction: a first group is based on methods of estimating unidimensional (along the wellbore profile) distribution of pore pressure, and a second group is based on 3D basin model solutions. The overpressure is a part of the rock pressure distributed to the fluid component of sedimentary rock, wherein the fluid component refers to liquid and/or gas component of the rock.
A first approach (see e.g. Magara K., Compaction and fluid migration, 1978, Elsevier Scientific Publishing Company, p. 319) uses empiric relationships between overpressure and porosity-sensitive well log and/or seismic data. Besides inherent low resolution and signal/noise restrictions of seismic reflections accessible in target intervals (2-4 km) (see e.g. Dutta N. C., Geopressure prediction using seismic data: current status and the road ahead. Geophysics, 2002, volume 67, No. 6, p.p. 2012-2041), the common shortcomings of all existing empiric methods are their restricted validity and non-adaptive framework. A main reason for this is the formal data fitting concept implemented therein. The quality of the background model in this concept has secondary priority in comparison with the uniqueness and speed of data transformations (type of fitting functions, method of approximation, flexibility, etc.) predefined in an empiric formula. From the geo-fluid system analysis point of view, the background earth models in this strategy are often oversimplified and inadequate. By way of example, the classic uniaxial effective stress approaches (see e.g. Terzaghi K., Peck R. B., Soil Mechanics in Engineering Practice, 1948, Wiley, New York, 566 page, or Eaton B. A., The Equation for Geopressure Prediction from Well Logs, 1975, SPE paper 5544) are essentially a unidimensional (1D) static approximation of a complex multi-mechanism phenomenon that gives rise to overpressure.
Modern modifications of these classic methods improve their flexibility, but do not change the focus onto rock compaction phenomena (Alberty R. W., Emerging trends in pressure prediction, scientific report at Offshore Technology Conference, May 5-8, 2003, Huston, USA, OTC 15290). The relevant earth models have significant restrictions of validity in depth, formation age and formation lithology; namely, they may be applicable only for shallow parts of sections represented by young and mostly clay sediments. However, the formation pressure and associated parameters of sedimentary rock essentially result from a combined effect of fluid retention and expansion mechanisms. The contributions of different factors change during sedimentation history, and within a single formation from one position to another. Therefore, no parameter influencing final formation pressure can be fixed by empirical formula-based approach. So, the typical problems rising before each prediction based on the first group of approaches relate to poor understanding of overpressure mechanisms acting within the area and lack of ways to give priority to the key coefficients.
The basin model based technologies, in contrast with the first group of methods, are based on a geo-fluid system analysis approach. This involves much more sophisticated dynamical Earth models (Guidish T. M., Kendall C. G. St. C., Lerch I., Toth D. J., Yarzab R. F., Basin Evaluation Using Burial History Calculations: an Overview. The American Association of Petroleum Geologists Bulletin, 1985, volume 69, No. 1, pages 92-105; Learch I., Theoretical Aspects of problems in basin modeling in “Basin Modelling Advances and Applications” 1990, Norwegian Petroleum Society, Special publication 3, Elsevier, Amsterdam, p.p. 35-65) which are based on differential operators describing global and local processes in basin time scale. The basin time scale, also referred to as geological time scale, is a time scale expressed in millions of years with time-step intervals from tens to hundreds of thousands of years. The use of well-grounded physical and chemical laws and respective model assumptions ensure that this approach exploits and encapsulates a deeper understanding of the present-day geo-fluid system state and in particular overpressure phenomena.
Still successful use of basin models for prediction of geo-fluid system properties and in particular for pre-drill overpressure prognosis with real-time drilling applications has been problematic to achieve up to now. The reason for this is the mathematical complexity of the relevant forward modeling operators and the absence of an adequate link between the calibration data and tunable model parameters. In other words, basin model solutions appear to be rather cumbersome for calibration by inverting data in terms of model parameter requirements (grid dimension, linear independence of parameters, etc.) and computational complexity of relevant 3D forward modeling operators. In addition, non-linear behavior of relevant forward model operators defined on regular 3D grids takes place because of the need to specify multiple dependent model parameters for each cell. Thus, conventional full-scale 3D basin models cannot be used in real-time.
Consequently there is a need for a method for generating a 3D earth model, which method would combine advantages and overcome shortcomings of the known approaches described above, in particular which could allow construction of an earth model suitable for real-time calculations, like empiric models, and have adequate validity, like basin models, and enable real-time data inversion.